An attempt to show how applications of pure mathematics can work in social sciences.

1.

Great French mathematician Andre Weil ( 1906 - 1998 ) is well known in history of social anthropology. In fact, he was co-author of Levi - Strauss 's The elementary structures of kinship and his a very short algebraic introduction in Levi-Strauss solution is contained in LS book on kinship. In 1940s Andre Weil was ready for such sort of collaboration with anthropologist. In 1920 he taught himself Sanskrit and had deep interests in Greek, Latin, correspondingly - Hinduism also. His number theoretical structuralism was connected with the mathematical separation of the infinite descent argument into 2 types in newly created Algebraic Geometry. However, after publication of LS book their cooperation became less intensive and Levi-Strauss changed his research direction to Trubetskoy - Jacobson's linguistics. Today, nevertheless, it could be interesting to introduce another unknown Weil's mathematical findings and theorems in theoretical anthropology.

2.

Another masterpiece of Weil is his theorem on representation of irrational numbers which has remarkable applications in mathematical geography, comparative demography and comparative company assessments in international business. I try to apply Weil's theorem for Brexit prediction.

Theorem. Let the first digits of number 2^n, where n =0;1;2;....Then statistics of their distribution is Weilian or 1;2;4;8;1;3;6;1;2...

Demonstration. Number 1 has a statistical weight 29%, 2 has 21%, 3 has 11%, 4 has 10%, 5 has 6%, 6 has 6%, 7 has 8%, 8 has 3% and 9 has 6%.

In 1980s Konstantinov and Arnold in 1997 showed that distribution of areas and populations in current national boundaries is Weilian .For example, Weil's index or relation of area : population for France is  5/6; UK 2/6; Italy 3/6; Ukraine 6/4; Georgia 6/4. It is very remarkable that our highly abstract theorem is able to catch essential characteristics of reality. Indeed, two currently disintegrated nations - Ukraine and Georgia have the same Weil Index!

Prediction. In comparison with Weil index for disintegrated nations, Italy and UK have some kind of reserve of stability - UK 2/6 and Italy 3/6. Thus, it could be difficult to represent UK in some deepest fundamental spatial sense as disintegrated nation. Hence, any kind of referendum of Brexit type cannot change status quo and it is quite logical that  on 23.06.2016 majority of UK population must vote STAY in the EU community.

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Michael,

Very interesting. But how does the mathematical model account for the facts that (1) in Britain, the Brexit vote produced a narrow majority in favor of Brexit and (2) that Hillary
Clinton has won a popular majority but still lost the election due to the peculiarities of the American Republic and its Electoral College? How would you refine your model to account for this difference?




Michael Alexeevich Popov said:

Let us continue our systematic work...

ANALYSIS OF OUR SUCCESSFUL PREDICTION.

Essential steps:

Step 1 (27 June)

Brexit is defined as a very rare unpredictable "Black Swan" (BS) ( in Taleb's sense ) event which can produce series of unpredictable events of bounded rationality.

Step 2. (4 July)

Attempt to develop some kind of mathematical theory ( intuitive prediction is not scientific  ) where Brexit is considered as highly unlikely ( for professional observers ) event that can totally alter the trajectory of the political system.

Step 3. (Aug 26)

In the search of BS manifestations. Brexit can have unexpected development in USA - assumption.

Step 4.(Sept 24)

Attempt of formalisation. Trump/ USexit function is introduced

Step 5.(Nov 2)

Refinements. Black Swan has own unknown exotic math?

Step 6.(Nov 7)

Logical structure of BS. Reference to B.Malinowski' functional analysis. US Black Swan may have logical structure of Banach paradox

Step 7.(Nov 9)

Observation of Black Swan. What appear to be small risks ( for professional observers, liberal social scientists , developers of liberal narrative and old paradigm politicians) accumulated to certain irreversible harm. Trump is obvious winner.

John, thanks

Mathematically, Brexit and Trump have similarity. Gap between two sides was strangely minimal, about 2-3 before event ( 24 Sept ). Hence highly unlikely event of Black Swan type is arising...For majority of professional observers it was like revolution. Even you probably was affected by speed and unpredictability of the last event. I'd like to say that Taleb tried to use nonexact statistical model for description of BS. I think we need to improve his math. In particularly, similar with modern theoretical physics ( in Malinowski spirit ) I 'd like to develop quantum - like simulation of BS events, hence to introduce pure mathematical corrections.



John McCreery said:

Michael,

Very interesting. But how does the mathematical model account for the facts that (1) in Britain, the Brexit vote produced a narrow majority in favor of Brexit and (2) that Hillary
Clinton has won a popular majority but still lost the election due to the peculiarities of the American Republic and its Electoral College? How would you refine your model to account for this difference?




Michael Alexeevich Popov said:

Let us continue our systematic work...

ANALYSIS OF OUR SUCCESSFUL PREDICTION.

Essential steps:

Step 1 (27 June)

Brexit is defined as a very rare unpredictable "Black Swan" (BS) ( in Taleb's sense ) event which can produce series of unpredictable events of bounded rationality.

Step 2. (4 July)

Attempt to develop some kind of mathematical theory ( intuitive prediction is not scientific  ) where Brexit is considered as highly unlikely ( for professional observers ) event that can totally alter the trajectory of the political system.

Step 3. (Aug 26)

In the search of BS manifestations. Brexit can have unexpected development in USA - assumption.

Step 4.(Sept 24)

Attempt of formalisation. Trump/ USexit function is introduced

Step 5.(Nov 2)

Refinements. Black Swan has own unknown exotic math?

Step 6.(Nov 7)

Logical structure of BS. Reference to B.Malinowski' functional analysis. US Black Swan may have logical structure of Banach paradox

Step 7.(Nov 9)

Observation of Black Swan. What appear to be small risks ( for professional observers, liberal social scientists , developers of liberal narrative and old paradigm politicians) accumulated to certain irreversible harm. Trump is obvious winner.

LIST OF POLITICAL EVENTS PROBABLY SHAPED BY BLACK SWAN - TYPE EVENTS

2016 - 2017

1.Brexit - total EU exit

2.Scotland independence referendum - UK drama

3.Trump USexit

4.China - USA conflict

5.NATO - Russia military conflict

6.Elections in Germany and France

7.Attempt of US civil war

8.EU collapse

9.Unknown highly unlikely event.

I am not sure what to make of "shaped by black swan type events." As opposed to being black swan events.

It could be shaped - because nobody knows exact form of curve in future BS events. I used different way of scientific based predictions. In comparison successful Cambridge group ( Oraclum Intelligence systems ) applied Bayesian Adjusted Social Network or BASON survey, based on experience of  Facebook studies of social networks between friends.

Black Swan came as an absolute shock to many. Professionals and expert communities estimated high probabilities for a Clinton victory. It is essential for understanding of BS class of mathematical objects in future.

The difficulty is separating true Black Swans, totally unexpected events, from rare but predictably rare events, especially when there is negligence in the model from which criteria are taken.

The Fukushima reactor meltdown following the Great East Japan Earthquake is an example of the latter. Engineering decisions were made on the assumption that certain events were so unlikely as to not be worth the cost of consideration while stones marketing the extent of a similar earthquake and tsunami only a century earlier were visible in the hills surrounding the site. And some decisions, e.g., locating the diesel generators to provide reserve power seaward of the reactor instead of above it in the hills, were just plain stupid. 

Now we know that a few individuals did, in fact, predict a Trump victory. Were they unusually perceptive or like the famous clocks that, however broken, are always right twice a day? 

Taleeb is right, I believe, to focus less on the probability of an event and more on the cost if it happens.

As you know both mathematicians and anthropologists usually try to understand new phenomena in the field, or to find new simulations in the laboratory. My limited experience of understanding and prediction of BS events in policy in some sense is different from Taleb's applications in arrival time of an aircraft, hidden risks of famine, nonlinearities in a porcelain coffee cup and similar effects of Taleb's fragility and antifagility ( fragility transfer theorem 2012), geology etc. Taleb made no reference to quantum - like Black Swan effects at all. My experience suggests it is very important. Hence, when Taleb says that the main problem behind BS is the limited understanding of model or representation error, it is right only in some particular sense.

ITALY 4 / 5.12.2016

An attempt to prevent new independence movements in Italy was failed.

Taleb's Fragility transfer theorem (2012) needs some reinforcement -  effect of self - reproducing Black Swans is possible.

RUSSIAN HACKERS FATAL INFLUENCE & TRUMP.

Some years ago I presented at OAC my results on Complexity Anthropology where field anthropologist equipped with modern Computational Complexity theory is able to see ethnographic reality in some unexpected rational context ( " P vs NP problem in the field anthropology"). I believed it could be very " futuristic" for today's anthropologists, however, after publication of US intelligence report on Trump's victory ( 7.1.17 ) I realized that my "futuristic" work has a sense.

The joint assessment of the CIA, the FBI and the National Security Agency was that "Russian hackers fatal influence "undermine public faith in the US democratic process ; denigrate Secretary Clinton and harm her electability and potential presidency.

Speaking Anthropologically - Mathematically, Russian hackers fatal influence must be based on successful solving P vs NP problem ( providing so called "Golden ticket" for hacking all thinkable computer systems ),technically - solving NP complete problems of STP type ( Travelling Trader problem ) with the list of million points... However, if even Government's  hackers have such sort of Golden ticket / quantum like algorithm, who can prove it?

I think, "old "social sciences cannot explain such sort of random matrix, and sooner or later some elements of "futuristic" experimental anthropology could be introduced in anthropological education.

TRUMP : COLLECTIVE ILLUSIONS OF WESTERN ANTHROPOLOGISTS.

Similar with pre - Renaissance science in Europe when proto- anthropology as a part of natural philosophy was dominated by dogma, religious authority and superstition, post - Trump's anthropology demonstrates remarkable similarity - anthropologists believe that USA is populated by robots without free will, democracy dogma and  anti - Russian superstitions became unspeakable paradigm in so called " normal " social sciences.

However, for business community it is obviously, that there is free will of voters in USA, Trump  who is equipped with the 3d Platform skills ( highly calculated  methods, digital marketing of brand - voters communications, mobile computations and intuitionistic math ) can be more competitive than any Clinton with old - fashioned  19 century social and political   scientists.

UNEXPECTED  EVENT.

Brexit and Trump produced some kind of  unseen "field of uncertainty "  where even insignificant event can create Big Sequences of unexpected events ( what I called as "Swan Lake" effect ). After Trump's claim " to return Crimea  to Ukraine " (= claim to start civil war in Russian Federation in many - steps logic ) - President Putin made involuntary step to recognise Donbass republic independence as well as to stop genocide of Russian speaking people of  Eastern Ukraine - today.

This insignificant step can produce fundamental consequences - new unseen randomness is arising. It must change geopolitical - and - mathematical landscape of the field of uncertainty dramatically...

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